[SymeAaro (OP)]

This is going to sound weird and stuff, but I’ll go for it.
Gravitational force is equal to: G((m1xm2)/rxr). Which means th force of gravity on me by the Earth is the same as the gravitational force on the Earth by me.
So do I weigh the same as the Earth? Or am I missing something?

[Kryptid]

If you weigh 150 pounds (just a random number), then you are pushing on the Earth with 150 pounds of force and the Earth is pushing back on you with 150 pounds of force as well.

Another way to look at this is to think of yourself as the planet and the Earth as an object that is being weighed on you. Although you have an extremely tiny gravitational field, the Earth is extremely massive so that the total weight actually evens out to a moderately-sized number (150 pounds). You weigh the same on the Earth as the Earth weighs on you.

[evan_au]

do I weigh the same as the Earth? Or am I missing something?

The concept of "weight" implies some standardised measurement conditions, usually "At sea level, on Earth.".

So if you change the measurement conditions, the measured weight changes.
- You weigh about 1/6 on the Moon as you do on the Earth
- If you are floating in space, and the Earth is floating in space, you are both weightless, and you weigh the same as the Earth
- If you measure the weight of you on the Earth, and the weight of the Earth on you, both come out as the same number. But you you are measuring both things under radically different conditions, so they are not really comparable.
- But if you put both the Earth and yourself level with the cloud-tops on Jupiter, the Earth would weigh far more than you. This is because you are measuring the weight of the Earth and the weight of yourself under the same conditions - ie at the same distance from Jupiter's center of mass. And the mass of the Earth is far greater than the mass of SymeAaro.

PS: The metric system sidesteps this dilemma by talking about the Mass of an object (measured in kilograms), which is a property of the object, regardless of whether it is on Earth, free-floating in space, on the Moon or on Jupiter.
There is a separate unit of Force (measured in Newtons) which measures the pressure you apply on the Earth, and which the Earth applies on you.

[jeffreyH]

The gravitational field strength of a person is far less than that of the earth at equal radial distances from the centre of mass of each of them. If the mass of the person were all within its own Schwarzscild radius then there would be a radial distance from its event horizon where the gravitational field strength would equal that at the surface of the earth. If the surface of the earth were at this radial distance from the centre of the black hole then the person would weigh the same as the planet. However, the definition of person is now lost.

[jeffreyH]

Be warned! The above scenario takes the definition of weight to absurd extremes.

[Janus]

The gravitational field strength of a person is far less than that of the earth at equal radial distances from the centre of mass of each of them. If the mass of the person were all within its own Schwarzscild radius then there would be a radial distance from its event horizon where the gravitational field strength would equal that at the surface of the earth. If the surface of the earth were at this radial distance from the centre of the black hole then the person would weigh the same as the planet. However, the definition of person is now lost.

No.  If our hypothetical person were compressed to an sphere with a radius of ~1.38e-5 m, then his surface gravity would be ~ 1g.    However, this does not mean that the force between himself and the Earth as a whole would increase by any significant amount.  If he were resting on the surface of the Earth, only that part of the Earth's surface touching him would be subject to that 1 g pull.  His gravitational pull is still subject to the inverse square law.  Any part of the Earth 2.76e-5 m away from his center would only experience 1/4 g.  At 5.52e-5m  this falls to 1/8g etc.  at the distance of the center of the Earth it will have fallen to ~4.6e-24g
The total "weight" felt by the "person" would be the result of the integration of the gravitational pull on all the different parts of the Earth, and would still add up to ~150 lbs.  The only small increase seen would be due to the fact that the center of mass for the compressed sphere would be just the slightest bit closer to the center of the Earth then the full-sized person would be.

[jeffreyH]

Nowhere did I say that the person sized black hole had the potential to move the earth. It"s field strength is very much less than that of the earth.

[Zer0]

A bit Off Topic post. ✌

Earth mass (M⊕, where ⊕ is the standard astronomical symbol for planet Earth) is the unit of mass equal to that of Earth. This value includes the atmosphere but excludes the moon. The current best estimate for Earth mass is M⊕ = (5.9722±0.0006)×1024 kg.

Some Interesting/Amusing examples. 👌

Net gains. 👍

In-falling material
Cosmic dust, Cosmic rays, meteors, comets, etc. are the most significant contributor to Earth's increase in mass. The sum of material is estimated to be 37,000 to 78,000 tons annually.

Global warming
Nasa has calculated that the Earth is gaining energy due to rising temperatures. It has been estimated that this added energy increases the mass of Earth by a tiny amount – 160 tonnes per year.

Solar energy conversion (minuscule)
Solar energy is converted to chemical energy by photosynthetic pigments as plants construct carbohydrate molecules. This stored chemical energy represents in increase in mass. Most of the chemical energy is reconverted into heat and then lost (radiated) through chemical processes, but some is sequestered and becomes biomass or fossil fuel.

Artificial photosynthesis (minuscule)
Can also theoretically add mass, assumed to be negligible but added for sake of completeness.

Heat conversion (probably minuscule)
Some outbound radiation is absorbed within the atmosphere by photosynthetic bacteria and archaea, including from chlorophyll f, which bind the energy into matter in the form of chemical bonds.

Net losses. 👎

Atmospheric escape of gases.
About 3 kg/s of hydrogen or 95,000 tons per year and 1,600 tons of helium per year are lost through atmospheric escape.

Spacecraft on escape trajectories (minuscule)
Spacecraft that are on escape trajectories represent an average mass loss at a rate of 65 tons per year. Earth lost about 3473 tons in the initial 53 years of the space age, but the trend is currently decreasing.

Human energy use (minuscule)
Human activities conversely reduce Earth's mass, by liberation of heat that is later radiated into space; solar photovoltaics generally do not add to the mass of Earth because the energy collected is merely transmitted (as electricity or heat) and subsequently radiated, which is generally not converted into chemical means to be stored on Earth. In 2010, the human world consumed 550 EJ of energy, or 6 tons of matter converted into heat, then almost entirely lost to space.

Deceleration of Earth's core (minuscule)
As the rotation rate of Earth's inner core decelerates, it loses rotational kinetic energy, which equates to a loss of 16 tons per year. However, this rotation speed has been shown to fluctuate over decades.

Non photosynthesizing life forms consume energy, and radiate as heat.

Natural processes (probably minuscule)
Events including earthquakes and volcanoes can release energy as well as hydrogen, which may be lost as heat or atmospheric escape.

Radiation Losses(minuscule)
From radioisotopes either naturally or through human induced reactions such as nuclear fusion or nuclear fission amount to 16 tons per year.

Additional human impact by induced nuclear fission
Nuclear fission, both for civilian and military purposes, greatly speeds up natural process of radio decay. Some 59,000 tons of uranium was supplied by mines in 2013. The mass of the uranium is reduced as it is converted to energy during the fission reaction.

Courtesy & Credits - Wikipedia. 👏

https://en.m.wikipedia.org/wiki/Earth_mass

[PmbPhy]

The concept of "weight" implies some standardised measurement conditions, usually "At sea level, on Earth.".

What a wonderful response. I sure missed you Evan, even though you royally ticked me off the last time I was here I still missed you.

[Bill S]

.....even though you royally ticked me off the last time I was here.....

I missed that.  Sounds like it could have been fun. 

[PmbPhy]

.....even though you royally ticked me off the last time I was here.....

I missed that.  Sounds like it could have been fun. 

No! Far from fun. Dangerous. Risk of life and limb dangerous.

I've gotten over it so lets not make a big deal of it. I sent you a PM explaining.

[Bill S]

Pete, you realised I was not serious?